In the Aharonov–Bohm setup, a double-slit experiment, when a long but thin solenoid of current is introduced between the two coherent beams of electrons behind the slits, an extra phase difference between the interfering beams appears, as shown by a shift in the interference pattern. This mysterious effect purportedly arises owing to an electromagnetic momentum, attributed to the presence of a vector potential at the location of either beam, due to the solenoid of current even when the magnetic field is zero outside the solenoid. It has remained a puzzle, how mere potential, thought to be just a mathematical tool for calculating electromagnetic field, can give rise to electromagnetic momentum in a system. Experimentally, the effect has been amply verified, with hardly any doubts that the observed effect is real. A satisfactory physical explanation of the existence of momentum, at least under the aegis of classical electromagnetism, is still missing since inception of the idea more than half a century back. We show here the presence of electromagnetic momentum in the product of the drift velocities of the current-carrying charges within the solenoid and the mass equivalent of their potential energies in the electric field of the external charges.
In the Aharonov–Bohm setup, a double-slit experiment, when a long but thin solenoid of current is introduced between the two coherent beams of electrons behind the slits, an extra phase difference between the interfering beams appears, as shown by a shift in the interference pattern. This mysterious effect purportedly arises owing to an electromagnetic momentum, attributed to the presence of a vector potential at the location of either beam, due to the solenoid of current even when the magnetic field is zero outside the solenoid. It has remained a puzzle, how mere potential, thought to be just a mathematical tool for calculating electromagnetic field, can give rise to electromagnetic momentum in a system. Experimentally, the effect has been amply verified, with hardly any doubts that the observed effect is real. A satisfactory physical explanation of the existence of momentum, at least under the aegis of classical electromagnetism, is still missing since inception of the idea more than half a century back. We show here the presence of electromagnetic momentum in the product of the drift velocities of the current-carrying charges within the solenoid and the mass equivalent of their potential energies in the electric field of the external charges.
In the Aharonov-Bohm setup, a double-slit experiment, coherent beams of electrons passing through two slits form an interference pattern on the observing screen. However, when a long but thin solenoid of current is introduced behind the slits between the two electron beams, an extra phase difference between them appears, as shown by a shift in the interference pattern. This happens even though there is no magnetic field outside the solenoid, at the location of the beams. This is known as Aharonov-Bohm effect, though the idea was mooted apparently a decade earlier, and the effect sometimes is called Ehrenberg-Siday-Aharonov-Bohm effect. This mysterious effect, purportedly arises owing to an electromagnetic momentum, attributed to the presence at the location of either beam, a vector potential due to the solenoid of current even when there exists no magnetic field outside the solenoid. The first experimental confirmation came soon and It has since been amply verified using clever experimental setups, leaving hardly any doubts that the observed effect is real. However, on the theoretical side the picture is not so clear and a satisfactory physical explanation of the existence of momentum, at least under the aegis of classical electromagnetism, is still missing since inception of the idea more than half a century back. It has remained a puzzle, how just potential, thought to be a mere mathematical tools for calculating electromagnetic field, can give rise to an electromagnetic momentum in a system, in lieu of field itself. We here show that a subtle momentum can be seen to lie in the product of the drift velocities of the current carrying charges and the mass equivalent of their non-localized potential energies in the electric field of the interfering electrons, which manifests, from a classical point of view, a linear momentum in the system. It is this hard-to-pinpoint, additional momentum, reflected through an extra phase difference between the interfering beams of electrons, which exhibits from a classical physics perspective, the presence of an elusive, long sought-after electromagnetic momentum in the system.
In the context of the Aharonov-Bohm effect, it is well-known that the local action of the vector potential or the non-local action of the magnetic field are properties attributable to quantum physics, which can explain the observed Aharonov-Bohm phase. Here we point out that, surprisingly, these properties are also attributable to classical physics and that this result follows from examining the electromagnetic angular momentum of a static electric charge outside an infinitely-long solenoid of finite radius carrying a uniform magnetic flux. This angular momentum may be expressed in three equivalent forms. The first form shows that there is an electromagnetic angular momentum even in regions for which the magnetic field vanishes but the potential does not, which stresses the physical nature of the vector potential in classical physics. The second form shows that there is an electromagnetic angular momentum produced by the non-local action of the magnetic field. The third form shows that the Aharonov-Bohm phase is proportional to the magnitude of the electromagnetic angular momentum, which sheds light on the physical meaning of this phase.
The AB (Aharonov-Bohm) effect is a pivotal quantum mechanical phenomenon that illustrates the fundamental role of the electromagnetic vector potential A in determining the phase of a charged particle's wave function, even in regions where the magnetic field B is zero.This effect demonstrates that quantum particles are influenced not only by the fields directly present but also by the potentials associated with those fields.In the AB effect, an electron beam is split into two paths, with one path encircling a solenoid and the other bypassing it.Despite the absence of a magnetic field in the regions traversed by the beams, the vector potential A associated with the magnetic flux through the solenoid induces a phase shift in the electron's wave function.This phase shift, quantified by qc , manifests as a change in the interference pattern observed in the detection screen.The phenomenon underscores the principle of gauge invariance in QED (quantum electrodynamics), where physical observables remain invariant under local gauge transformations of the vector and scalar potentials.This reinforces the notion that the vector potential A has a profound impact on quantum systems, beyond its classical role.This article outlines the AB effect, including its theoretical framework, experimental observations, and implications.The focus on the role of the vector potential in quantum mechanics provides a comprehensive understanding of this important phenomenon.
In the usual Aharonov-Bohm effect, representing an especial case of the Berry phase phenomenon, classical magnetic field within long and thin solenoid (or classical vector potential of the electromagnetic field without this solenoid) causes phase difference and interference shape translation of the quantum propagating (external) electron. In this work we consider a variation of the usual Aharonov-Bohm effect with two solenoids sufficiently close one to the other so that (external) electron cannot propagate between two solenoids but only around both solenoids. Here magnetic field (or classical vector potential of the electromagnetic field) acting at quantum propagating (external) electron represents the quantum mechanical average value or statistical mixture. It is obtained by wave function of single (internal, quantum propagating within some solenoid wire) electron (or homogeneous ensemble of such (internal) electrons) representing a quantum superposition with two practically non-interfering terms. All this implies that phase difference and interference shape translation of the quantum propagating (external) electron represent the quantum mechanical average value or statistical mixture. In this way we obtain a very interesting generalization of the usual Aharonov-Bohm effect and Berry phase concept. As it is well-known in the usual experimental arrangement corresponding to the AharonovBohm effect [1]-[4] (representing an especial case of the Berry phase phenomenon [4], [5]) behind a diaphragm with two slits there is a long and very thin solenoid (placed perpendicularly, i.e. in the z-axis direction, to the x-0-y plane of the propagation of the (external, without solenoid
In 1959, Yakir Aharonov and David Bohm pointed out an experiment that should be impossible according to the standard intuitions of classical electromagnetism. A charged particle is sent through a double‑slit apparatus with a long thin solenoid placed between the two paths. The solenoid contains a magnetic field; the regions traversed by the particle do not. In classical mechanics, the particle should be entirely unaffected — no force, no torque, no Lorentz coupling. The interference pattern should be unchanged whether the solenoid is on or off. It isn't. When the solenoid is energized, the interference pattern shifts by Δφ = (q/ℏ) Φ, where Φ = ∫B·dA is the magnetic flux threading the solenoid. The particle’s wavefunction registers a region of magnetic field through which the particle never travels. Chambers performed the experiment in 1960; Tonomura confirmed it definitively with superconducting measurements in 1986. The effect is now standard textbook material and one of the deepest empirical phenomena in quantum mechanics. The puzzle is structural. In classical electromagnetism, the magnetic vector potential A was treated as a mathematical convenience — a quantity from which B = ∇×A could be computed but with no independent physical reality. The AB effect breaks this picture: the interference shift depends on ∮A·dx around the closed path, a gauge‑invariant integral that is non‑zero in regions where B = 0. The vector potential carries physical information that the magnetic field alone does not. Standard QM accommodates this by accepting that A is the physically meaningful quantity in the quantum context. This works mathematically but leaves a deeper question open: why should A have physical reality at all? This walkthrough shows how the Event Density framework provides an answer through Theorem 17. T17 establishes that gauge fields are the continuum‑level appearance of the substrate’s rule‑type connection — the substrate object that carries rule‑type label information from one substrate region to another. The gauge potential is not a mathematical convenience; it is the substrate’s parallel‑transport infrastructure for the rule‑type relabeling group. The AB phase is the integral of this substrate connection around a non‑contractible loop in a multiply‑connected substrate channel — a substrate‑level monodromy with observable consequences whenever the substrate’s topology supports closed loops the wavefunction can wind around. Stokes’ theorem connects the monodromy to the enclosed flux: Δφ = qΦ/ℏ. The structural payoff: the AB phase is not a mysterious nonlocal effect of the gauge potential. It is the substrate‑level monodromy of the rule‑type connection around a closed loop in a multiply‑connected substrate region. The gauge potential’s physical reality is not a postulate; it is what T17 establishes the substrate to provide.
The traditional Aharonov Bohm effect (AB effect) attributes the light and dark fringes on screen to phase interference of electron matter wave. It presumes that the magnetic field outside the solenoid equals zero and particles receive no force. This system has long served as key support for wave particle duality. This paper completely abandons the hypothesis of wave interference and quantum phase. It establishes the model of electron vibrating point particle to reveal the real physical mechanism of AB effect. Fringes are not superposition product of waves. They are formed by differential deflection of charged electrons under magnetic force and Coulomb repulsion, followed by regular superposition of two upper and lower particle beams. Both magnetic force and Coulomb repulsion are long range forces. They only differ in effective action range and variation rule of force with distance. Comparative experiments using direct current solenoid and direct current long straight wire can falsify the unrealistic assumption that magnetic field outside coil cancels out to zero. Supporting single side shielding verification experiment can directly test the correctness of orthodox quantum interpretation. Electrons have no wave property. As long as point particles with inherent vibration are modulated by field, they can form fringe similar to interference fringe. Photons are also point particles with inherent vibration. When photons pass through slits, they interact with slit wall and produce deflection, so as to form photon diffraction and interference fringes. The hypothesis of wave particle duality is invalid.